1. Field of the Invention
The invention relates generally to pattern recognition systems and, more particularly, but not by way of limitation, it relates to an improved digital process for representation and detection of specific waveforms extracted from seismic signal data in the presence of noise.
2. Description of the Prior Art
The prior art attempts at the extraction of common signals have been conbined to a single group of signals. One well-known prior method is that known as "stacking" or "weighted stacking." One form of this technique is proposed in such as W. H. Mayne, "Common Reflection Point Horizontal Stacking Techniques," Geophysics, Vol. 27, pp. 927-938, wherein it was suggested that a group of seismic signals may be combined by simple addition to provide a common signal estimation. Such simple addition does not extract optimally a common signal of a group of signals.
Another work of interest is that of Gimlim, Keener and Lawrence, "Maximum Likelihood Stacking in White Gaussian Noise With Unknown Variances," IEE Trans., Geoscience and Remote Sensing, Jan. 1982, pp. 91-98. Such maximum likelihood signal extraction technique requires numerical estimation of a large number of parameters, and it is a process that usually has convergence difficulties and whose solution depends upon the initial parameter values. Still other forms of maximum likelihood filtering of reflection seismograms have been carried out in a method which requires the knowledge of signal and noise spectral densities which, in most cases, are not available. All of these prior art approaches function with input of a single group of signals and they do not take into account such as correlations of signals between different groups of signals.
Several other prior sources treated the waveform recognition and classification problem. These teachings used time series models such as autoregressive models of certain order to represent the signals, and they then use the co-efficients of such models in a pattern recognition framework for the classification of signals. The difficulties associated with this approach are that the optimal model order may vary from trace-to-trace and the pattern recognition approach requires fixing of the model order. The discriminating information of the signals may not condense into the co-efficients of the autoregressive models. All such prior teachings view each trace independently and they do not take into account correlations between different signals of a single group or different signals of different groups in the estimation of model co-efficients. These prior teachings are exemplified by such as P. Bois, "Autoregressive Pattern Recognition Applied To The Delimitation of Oil and Gas Reservoirs," Geophysical Prospecting, Vol. 28, 1980, pp. 582-591.